D. Kirkwood—Motions of the Perihelia of Jupiter, etc. 225 
ART. XXIX.— On certain Relations between the mean motions of 
the Perihelia of Jupiter, Saturn, Uranus and Neptune; by 
Professor DANIEL KiIRKWOOD. 
In Mr. Stockwell’s able memoir* on the secular variations of 
the planary orbits, it is shown that the mean motions of the 
perihelia of Saturn, Uranus and Neptune are as follows: 
ET Tg oa iaige pine sem ge rennin Meunier cre ae 22’’.4608479 
AITADUOY 0, 53:5 15s baw eae 3.7166075 
Pieptune. i6:.icnvewew wt add ba ete” 0.6166849 
Denoting these values by Nvi, Nvi, and Nviii, respectively, 
we have, 
Nvi_7Nvii+ @Nviii = 0'.1447048, . . . (1) 
As these quantities depend upon the masses of the planets, some 
of which are not i i 
‘, Onigsberg astronomer, is 
176.55. Now, it will be found that a value of 177”.17 (which 
exceeds Bessel’s by 0”.62), corresponds to a mass, sz¢3 which 
Nvi_7Nvii+6Nvii=O, . . . (2) 
accurately true. The difference, 0.62, is less than that between 
the determinations of the equatorial diameter of Saturn by the 
est observers. 
If equation (2) be exact, the corresponding relation between 
the mean longitudes of the perihelia will be obvious, and it 
Must follow that the perihelia of no three of the four outer planets 
can simultaneously have the same mean longt _In short, if 
’, Li, Lvii and Lili, represent the mean longitudes of the 
Perihelia of Jupiter, Saturn, Uranus and Neptune, respectively, 
* Smithsonian Contributions, Washington, 1872. 
} The mean motion of Jupiter’s perihelion is precisely the same. 
AM. Jour. $o1.—Turrp Sariss, VOL. IV, No. 21.—SEPTEMBER, 1872. 
15 
